21 octobre 2026
Titre: Finite-Time Stabilization of Linear Systems via Optimal Control
Abstract: In this talk, an optimal control framework for achieving finite-time stabilization of linear systems is presented. By introducing a suitably constructed integral cost function, we derive a new class of nonlinear controllers that guarantee finite-time stability through the application of the optimality principle. The relationship between the resulting optimal control law and the associated value function is analyzed, leading to the derivation of a Hamilton–Jacobi–Bellman (HJB) equation and the study of its regularity properties. The link between HJB equation and finite-time stabilizing controllers is leveraged. An extension of the results to uniformly bounded controllers and practical feedback reconstruction using neural networks is discussed.